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GED Math : Midpoint Formula

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Example Questions

Example Question #21 : Midpoint Formula

Find the midpoint of the line connecting and .

Possible Answers:

(222,42)

(211,41)

(202,41)

(202,24)

Correct answer:

(211,41)

Explanation:

Find the midpoint of the line connecting and .

To find the midpoint, we will essentially average out our x and y values independently.

What this will look like is:

$(x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

So, all we need to do is find the average of each of our dimensions and we are set.

$(x_m,y_m)=(\frac{9+413}{2},\frac{17+65}{2})=(\frac{422}{2},\frac{82}{2})=(211,41)$

So, our answer is:

(211,41)

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Example Question #21 : Midpoint Formula

A line with endpoints (1, 4) and (a, b) has a midpoint at (5, 12) . What is the value of a+b ?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the midpoint of a segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Solve for :

$\frac{a+1}{2}=5$

a+1=10

a=9

Solve for :

$\frac{b+4}{2}=12$

b+4=24

b=20

Thus, a+b=9+20=29

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Example Question #121 : Coordinate Geometry

Find the midpoint of the line connecting the following points.

(19,47) (99,123)

Possible Answers:

(59,85)

(55,89)

(40,38)

(89,58)

Correct answer:

(59,85)

Explanation:

Find the midpoint of the line connecting the following points.

(19,47) (99,123)

To find the midpoint, we will use midpoint formula, which essentially averages out the x and y values of our points.

Midpoint formula:

$(x_m,y_m)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Now, plug in our points and solve!

$(x_m,y_m)=(\frac{19+99}{2}, \frac{47+123}{2})=(\frac{118}{2},\frac{170}{2})=(59,85)$

So, we have our answer:

(59,85)

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Example Question #23 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (-7, 5) and (10, -2) .

Possible Answers:

$(\frac{3}{2}, \frac{3}{2})$

$(\frac{15}{2}, \frac{17}{2})$

$(\frac{17}{2}, \frac{3}{2})$

$(\frac{2}{3}, \frac{3}{2})$

Correct answer:

$(\frac{3}{2}, \frac{3}{2})$

Explanation:

Recall how to find the midpoint of a line:

$(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Plug in the given points to find the midpoint.

$\text{Midpoint}=(\frac{-7+10}{2}, \frac{5+(-2)}{2})=(\frac{3}{2}, \frac{3}{2})$

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GED Math : Midpoint Formula

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #21 : Midpoint Formula

Example Question #21 : Midpoint Formula

Example Question #121 : Coordinate Geometry

Example Question #23 : Midpoint Formula

All GED Math Resources

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